Question

A line makes the same angle θ, with each of the x and z axis. If the angle β, which it makes with y-axis, is such that sin²β = 3sin²θ, then cos²θ equals:

(a) 3/5 

(b) 1/5

(c) 2/3 

(d) 2/5.

Answer 1

(a) : If a line makes the angle α, β, γ  with x, y, z axis respectively then
l² + m² + n² = 1
=> 2l² + m² = 1 or 2n² + m² = 1
=> 2cos²θ = 1 – cos²β (α = γ = θ)
2cos²θ = sin² β
=> 2cos²θ = 3sin²θ (given sin²β = 3sin²θ)
=> 5cos²θ = 3